# Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. y=sqrt(x - 2) - 1

Question
Performing transformations
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
$$y=sqrt(x - 2) - 1$$

2021-01-20
To determine:
Graph of $$y=sqrt(x−2)−1$$ by applying appropriate transformation.
Firstly, we will draw graph of $$y=sqrtx$$ which is given by:Y1
now, we will draw graph of $$y=sqrt(x−2)$$ by shifting the graph of $$y=sqrtx$$ two units towards right.
So, the graph of $$y=sqrt(x−2)$$ is as follows:Y2
Now, we will draw graph of $$y=sqrt(x−2)−1$$ by shifting the graph of $$y=sqrt(x−2)$$ one unit downward along y axis.
The graph of $$y=sqrt(x−2)−1$$ is given by:Y3

### Relevant Questions

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations. $$\displaystyle{y}={x}^{{{2}}}-{4}{x}+{5}$$
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations.
$$\displaystyle{y}={1}-{2}\sqrt{{{x}}}+{3}$$
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations. $$\displaystyle{y}={1}-{\frac{{{1}}}{{{x}}}}$$
Starting with the function $$f(x) = e^x$$, create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
$$f_1 (x) =$$?
ii. Then compress your result by a factor of $$1/7$$
$$f_2 (x) =$$ ?
iii. Next, reflect it across the x-axis.
$$f_3 (x) =$$ ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?
Graph by labeling three points and determine the type or types of transformations:
$$h(x)=sqrt(x-2)-1$$
Sketch the graph of the function $$f(x) = -2^x+1 +3$$ using transformations. Do not create a table of values and plot points
Explain how you could graph each function by applying transformations.
(a) $$y = log(x -2) + 7$$ (b) $$y = -3logx$$ (c) $$y = log(-3x)-5$$
Your friend attempted to describe the transformations applied to the graph of $$y=sinx$$ to give the equation $$f(x)=1/2sin(-1/3(x+30))+1$$.
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.
Create a new function in the form $$y = a(x-h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$.
Give the coordinates of the vertex for the new parabola.
g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?
Coordinates of the vertex for the new parabola are:
x=?
y=?
Create a new function in the form $$y = a(x- h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$